Lesson eLearning

Find the perpendicular distance of the point (0,5) from the line 3x-4y=12.

medium 2 marks Class 9 · Mathematics · Coordinate Geometry
Answer
32/5

The correct answer is 32/5 — Divide to obtain d = 32/5 = 6.4.

Step-by-step solution

  1. Rewrite the line in standard form 3x-4y-12 = 0.
  2. Use the point–to–line distance formula d = |Ax0 + By0 + C|/sqrt(A^2 + B^2) with A=3, B=–4, C=–12 and point (x0,y0)=(0,5).
  3. Compute the numerator: |3(0) + (–4)(5) + (–12)| = |0 – 20 – 12| = |–32| = 32.
  4. Compute the denominator: sqrt(3^2 + (–4)^2) = sqrt(9 + 16) = sqrt(25) = 5.
  5. Divide to obtain d = 32/5 = 6.4.
Common mistake: Missing absolute value or wrong denominator.

Concept tested: Distance from point to line.

Published · How this solution was prepared and checked

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